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Shape of the graph

Source: AHSME 1991 problem 18

October 22, 2011
conicshyperbolaparabolacomplex numbersAMC

Problem Statement

If SS is the set of points zz in the complex plane such that (3+4i)z(3+4i)z is a real number, then SS is a
<spanclass=′latex−bold′>(A)</span> right triangle<spanclass=′latex−bold′>(B)</span> circle<spanclass=′latex−bold′>(C)</span> hyperbola<spanclass=′latex−bold′>(D)</span> line<spanclass=′latex−bold′>(E)</span> parabola <span class='latex-bold'>(A)</span>\text{ right triangle}\qquad<span class='latex-bold'>(B)</span>\text{ circle}\qquad<span class='latex-bold'>(C)</span>\text{ hyperbola}\qquad<span class='latex-bold'>(D)</span>\text{ line}\qquad<span class='latex-bold'>(E)</span>\text{ parabola}
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